Obtaining Constitutive Relationship for Rate-Dependent Rock in SHPB Tests

A large number of tests have recently been conducted with the Split Hopkinson pressure bar (SHPB) method to determine the characteristics of rock dynamics. However, it is still impossible to get test results at a perfect constant strain rate from this set-up owing to the rate dependency of rock materials. For instance in most cases, dynamic behavior of rock can only be described with an average strain rate. The results from these methods, including rich strain rate information, frequently tend to be inexplicable or self-contradictory. The obtained stress–strain curves can then never be directly treated as constitutive curves as in static tests. In this paper, the reasons behind the controversial stress–strain results with current methods are analyzed. In addition, the requirement for the rock specimen to deform at a constant strain rate is demonstrated after theoretical analysis of correlations among specimen, deforming stress, incident stress, reflected stress and transmitted stress. With test results from SHPB by pulse shaper and special shape striker methods, the requirement is verified. Finally, the method of 3D scattergram considering stress–strain–strain rate simultaneously is brought up to get constitutive relationships of rate-dependent rock. The new method gives reasonable predictions for constitutive relationships of rock at different strain rates. At the same time, the new method has fewer requirements and has a wider application scope for SHPB tests.